Network Centrality Metrics Based on Unrestricted Paths, Walks and Cycles Compared to Standard Centrality Metrics

A key issue with standard network measures of closeness and betweenness centrality is that they rely on the shortest paths between nodes within the network structure, whereas the degree centrality only reveals the immediate neighborhood of a node. Furthermore, many measures found in the literature do not accurately represent the physical or probabilistic characteristics of nodal centrality, network flow, and other salient properties. For example, recurrent spreading in a network is often overlooked by these metrics. Standard centrality measures have limitations, being optimal for one application but not for others. Here, we present new metrics based on our influence spreading model to characterize network structure for various network science applications. These probabilistic measures account for all feasible walks and cycles in the network. We compare our new metrics with the standard metrics in terms of the node rankings given by different centrality measures, by examining scatter plots, and by using the Pearson correlation coefficient. In the influence spreading model, we define the in-centrality measure to characterize how central a node is as a target of influence by other nodes and the out-centrality measure to characterize how central a node is as a source of influence on other nodes. Our results show that the influence spreading betweenness centrality reveals the importance of alternative routes while maintaining similarity to standard betweenness centrality.